Fine Tuning of Defects Enables High Carrier Mobility and Enhanced Thermoelectric Performance of n-Type PbTe

High carrier mobility is critical to improving thermoelectric performance over a broad temperature range. However, traditional doping inevitably deteriorates carrier mobility. Herein, we develop a strategy for fine tuning of defects to improve carrier mobility. To begin, n-type PbTe is created by compensating for the intrinsic Pb vacancy in bare PbTe. Excess Pb2+ reduces vacancy scattering, resulting in a high carrier mobility of ∼3400 cm2 V–1 s–1. Then, excess Ag is introduced to compensate for the remaining intrinsic Pb vacancies. We find that excess Ag exhibits a dynamic doping process with increasing temperatures, increasing both the carrier concentration and carrier mobility throughout a wide temperature range; specifically, an ultrahigh carrier mobility ∼7300 cm2 V–1 s–1 is obtained for Pb1.01Te + 0.002Ag at 300 K. Moreover, the dynamic doping-induced high carrier concentration suppresses the bipolar thermal conductivity at high temperatures. The final step is using iodine to optimize the carrier concentration to ∼1019 cm–3. Ultimately, a maximum ZT value of ∼1.5 and a large average ZTave value of ∼1.0 at 300–773 K are obtained for Pb1.01Te0.998I0.002 + 0.002Ag. These findings demonstrate that fine tuning of defects with <0.5% impurities can remarkably enhance carrier mobility and improve thermoelectric performance.


■ INTRODUCTION
Thermoelectric materials can effectively utilize low-grade heat sources to generate electricity, such as industrial waste heat, automobile exhaust, solar energy, geothermal heat, etc. 1−4 To date, the priority of thermoelectric research is to improve the conversion efficiency for more widespread applications. The conversion efficiency depends on the dimensionless figure of merit ZT, ZT = S 2 σT/κ, where S is the Seebeck coefficient, σ is the electrical conductivity, T is the absolute temperature in kelvin, and κ is the total thermal conductivity (κ = κ lat + κ ele + κ bi , where κ lat is the lattice thermal conductivity, κ ele is the electronic thermal conductivity, κ bi is the bipolar thermal conductivity). In general, thermoelectric enhancement relies heavily on a large Seebeck coefficient, high electrical conductivity, and low thermal conductivity. Nevertheless, the above three thermoelectric parameters are governed primarily by the carrier concentration and are not independently controllable, making them difficult to be optimized simultaneously. 5−9 Researchers have conducted in-depth and fruitful research in upgrading thermoelectric performance via combined optimization of electrical and thermal transport. For electrical properties, optimizing carrier concentration, 10−12 increasing carrier mobility, 13,14 and modulating band structure 15−19 are generally applied. For thermal properties, the traditional method is declining the lattice thermal conductivity via hierarchical structures, involving atomic-scale defects, 20−22 nanoscale defects, 23−25 and microscale defects. 26,27 Among a variety of thermoelectric materials, PbTe is a representative thermoelectric material servicing at medium temperature. Numerous research studies have shown that ptype PbTe materials have achieved extraordinary thermoelectric properties. Many prominent p-type PbTe systems have realized ZT > 2.0, such as Pb 0.98 Na 0.02 Te, 28 Pb 0.98 Na 0.02 Te−8% SrTe, 29 Pb 0.98 Na 0.02 Te−6%MgTe, 30 Pb 0.95 Na 0.05 Te−0.5% AgInSe 2 , 31 and Pb 0.075 K 0.025 Te 0.7 S 0. 3. 32 In contrast, their counterpart, n-type PbTe, shows lower ZT values because of the large energy offset (∼0.45 eV) between the conduction bands, so further improvement of n-type PbTe is needed to match p-type PbTe. With time, we discovered several optimization methods that could bring about considerable intensification in the thermoelectric performance of n-type PbTe, such as doping and band engineering. 33 However, even though traditional doping undoubtedly plays a significant role in increasing the carrier concentration, dopants inevitably reduce carrier mobility. 34−36 Band engineering, as another attractive and feasible method, facilitates electrical performance by boosting the effective mass, while it is also detrimental to the carrier mobility. 37,38 In general, these methods are capable of enhancing the maximum ZT, whereas a major drawback is their tendency to decrease carrier mobility, which limits the ZT ave . 39 To ensure good thermoelectric properties over a wide temperature range, comparable n-type PbTe systems with high carrier mobility must be developed.
In this work, fine tuning of defects in PbTe is successively carried out to improve the carrier mobility. First, a small amount of excess Pb (0.004−0.012) is introduced into PbTe. As Pb enters the intrinsic Pb vacancies, n-type PbTe with relatively low carrier concentration is obtained. The dwindling vacancy defects improve carrier mobility, and the maximum carrier mobility reaches ∼3400 cm 2 V −1 s −1 at 300 K in Pb 1.01 Te. Benefiting from the high carrier mobility, a maximum power factor of ∼31.3 μW cm −1 K −2 at 300 K is achieved in Pb 1.01 Te. Second, excess Ag is subsequently introduced to fill the remaining Pb vacancies. Results reveal that the comparatively low room-temperature carrier concentration of ∼5.5 × 10 17 cm −3 leads to a high carrier mobility of ∼7300 cm 2 V −1 s −1 , resulting in a further increased power factor of ∼39.3 μW cm −1 K −2 at 300 K for Pb 1.01 Te + 0.002Ag. In particular, Ag atoms in the Pb 1.01 Te system undergo a dynamic doping process with increasing temperatures, first compensating the Pb vacancies and then entering more interstitial positions due to the temperature-dependent solubility of Ag in the PbTe matrix, 40 which improves the carrier concentration from ∼5.5 × 10 17 cm −3 at 300 K to ∼8.5 × 10 18 cm −3 at 873 K for Pb 1.01 Te + 0.002Ag. Meanwhile, this unique dynamic doping behavior can effectively decouple the carrier concentration and carrier mobility across the entire temperature range and suppress bipolar diffusion at high temperatures. Last, 0.2% of I element (0.002I) is adopted to optimize the carrier concentration while maintaining superior carrier mobility than other n-type PbTe systems with similar carrier concentrations. Meanwhile, the minimum lattice thermal conductivity can reach as low as ∼0.5 W m −1 K −1 for Pb 1.01 Te 0.998 I 0.002 + 0.002Ag. As a result, a maximum ZT of ∼1.5 at 773 K and a high average ZT ave of ∼1.0 at 300−773 K are obtained for Pb 1.01 Te 0.998 I 0.002 + 0.002Ag.

■ EXPERIMENTAL SECTION
All raw materials used in the experiment were simple substances with more than 99.99% purity, including Pb, Te, Ag, and I. First, they were placed in quartz tubes according to the stoichiometric ratio. The quartz tubes were sealed below 10 −4 Pa and put into a furnace (slowly heating from room temperature to 1323 K for 24 h, holding for 10 h, and finally cooling to room temperature). After the temperature program finished, some silver ingots were obtained, which were then ground into powder for proceeding spark plasma sintering (SPS-211Lx, Dr. Sinter). Finally, the sintered cylindrical, small pieces were cut into rectangles of 10 mm × 3 mm × 3 mm and slices of 8 mm × 8 mm × 1.5 mm to perform electrical and thermal performance tests. The electrical performance was measured by Cryoall CTA (electrical conductivity, σ and Seebeck coefficient, S) and Lake Shore 8400 Series (carrier density, n) instruments. The thermal performance was tested by a Netzsch LFA 457 (thermal diffusivity, D). The thermal conductivity, κ, was estimated by κ = D × C p × ρ, where C p is the specific heat capacity based on Debye's law and ρ is the sample density calculated by the ratio of mass to volume. The optical band gap was measured by a Fourier transform infrared spectrometer, IRAffinity-1S, based on the infrared diffuse reflection method.

■ RESULTS AND DISCUSSION
In this study, the method of fine tuning of defects is used in the PbTe system to achieve superior electrical characteristics while maintaining a relatively low thermal conductivity. Supporting Information to create n-type PbTe, a modest quantity of Pb was first introduced, filling the intrinsic Pb vacancies, which increases carrier mobility and lowers thermal conductivity. Second, excess Ag is adopted for Pb 1.01 Te to fill the remaining Pb vacancies and also occupy interstitial sites, allowing the Pb 1.01 Te + xAg system to achieve higher carrier concentration, ultrahigh carrier mobility, and lower thermal conductivity simultaneously across the entire temperature range. Third, the Iodine element is adopted to enhance the carrier concentration, further improving the power factor and restraining the lattice thermal conductivity in the whole temperature range.
Thermoelectric Transport Performance of Pb 1+x Te. Figure S1a shows the powder X-ray diffraction (XRD) patterns of Pb 1+x Te (x = 0, 0.004, 0.006, 0.008, 0.01, 0.012), and the corresponding lattice parameters are given in Figure S1b. All Pb 1+x Te samples are NaCl-type cubic structures without extra diffraction peaks detected, and the lattice parameters increase slightly with excess Pb.
As can be seen in Figure 1a, the electrical conductivities decrease first and then increase with increasing Pb amount.
Correspondingly, Pb 1+x Te undergoes a p−n transition at low temperatures, as shown in Figure 1b. Specifically, the Seebeck coefficient of bared PbTe is positive at low temperatures; however, when x ≥ 0.008, the Seebeck coefficient is completely negative, resulting in n-type PbTe throughout the measuring temperature range. The combined behavior of electrical conductivity and Seebeck coefficient indicates that the hole concentration in PbTe is suppressed by excess Pb. In Figure  1c, benefitting from the improved electrical conductivity and Seebeck coefficient, the power factor is enhanced significantly, and the maximum value, i.e., room-temperature value, increases notably from ∼18.0 μW cm −1 K −2 for PbTe to ∼31.3 μW cm −1 K −2 for Pb 1.01 Te. In Figure 1d, the total thermal conductivity of PbTe reduces slightly with excess Pb, and the room-temperature value decreases from ∼2.1 to ∼2.0 Wm −1 K −1 caused by diminished lattice thermal conductivity, as shown in Figure 1e. Pb 1+x Te shows higher electronic thermal conductivity, as shown in Figure S2b, because excess Pb fills the intrinsic Pb vacancies, thereby creating weaker carrier scattering. Ultimately, an average ZT value of ∼0.5 for Pb 1.01 Te is obtained throughout the whole measuring temperature range, as shown in Figure 1f.
To understand the electrical transport evolution of Pb 1+x Te, we carried out the Hall measurement. In Figure 2a With the increasing Pb fraction, the carrier concentration is gradually elevated, indicating that more and more Pb enters Pb vacancies. Based on the inverse relationship between carrier concentration and carrier mobility, relatively low carrier concentration brings about high carrier mobility since reduced Pb vacancies alleviate the charge carrier scattering, and the maximum carrier mobility can reach ∼3400 cm 2 V −1 s −1 for Pb 1.01 Te. Figure 2b shows the atomic schematic diagram of the Pb 1+x Te system, graphically depicting the phenomenon that excess Pb atoms occupy the intrinsic Pb vacancies.
Electrical Transport Performance of Pb 1.01 Te + xAg. The powder X-ray diffraction (XRD) measurements of Pb 1.01 Te + xAg (x = 0−0.005) samples are performed, as shown in Figure S4a. All samples are NaCl cubic structures, and no peaks of impurities are found. Likewise, the small amount of excess Ag results in a slight expansion of the lattice parameters, as shown in Figure S4b. Figure 3 shows that excess Ag significantly improves the electrical transport performance of the Pb 1.01 Te + xAg system. Figure 3a shows a clear increase in electrical conductivity throughout the whole temperature range. In particular, the electrical conductivity increases anomaly above 500 K. In Figure 3b, the negative Seebeck coefficients prove that Pb 1.01 Te + xAg is electron-dominated n-type material. The introduction of Ag reduces the Seebeck coefficient, and the maximum absolute value decreases from ∼385.9 μV K −1 for Pb 1.01 Te to ∼249.0 μV K −1 for Pb 1.01 Te + 0.002Ag. The Pisarenko curve in Figure S5 reveals that the effective mass of the Pb 1.01 Te + xAg system remains approximately 0.22m 0 , indicating that the depressed Seebeck coefficient of Pb 1.01 Te + xAg is attributed to the elevated carrier concentration rather than the reduced effective mass. As a result, significantly incremental electrical conductivity and abated Seebeck coefficient further enhance the power factor compared to Pb 1.01 Te. In particular, a superior room-temperature power factor of ∼39.3 μW cm −1 K −2 is  acquired for Pb 1.01 Te + 0.002Ag, as shown in Figure 3c. Also, the power factor above 500 K is twice higher as that of Pb 1.01 Te. Figure 3d shows the carrier concentration and carrier mobility of Pb 1.01 Te + xAg at room temperature. Carrier concentration increases as the Ag fraction rises; however, carrier mobility is not impaired. Particularly, the maximum carrier mobility is increased by more than twice from ∼3400 cm 2 V −1 s −1 for Pb 1.01 Te to ∼7300 cm 2 V −1 s −1 for Pb 1.01 Te + 0.002Ag.
To get an insight into the remarkable electrical transport properties of Pb 1.01 Te + xAg, we measured the temperaturedependent carrier concentration, as shown in Figure 4a,b. The carrier concentrations of bare PbTe and Pb 1.01 Te increase with increasing temperatures, as shown in Figure S6, which is derived from the low carrier concentration and thus pronounced bipolar effect at high temperatures. 44 However, Pb 1.01 Te + xAg systems still exhibit increasing carrier concentration throughout the temperature range even though their bipolar effect is suppressed (the suppressed bipolar effect is evidenced by the low bipolar thermal conductivity, which is discussed in detail in the next section). We attribute the abnormal temperature-dependent behavior of carrier concentration to Ag-induced dynamic doping. 40 The dynamic doping process in Pb 1.01 Te + xAg is initiated by the multiple occupancies of Ag atoms with increasing temperatures, and Figure 4c displays the phenomena in detail. At 300−500 K, Ag atoms compensate for intrinsic Pb vacancies and interstitials, enhancing carrier mobility, as shown in Figure 4b. Above 500 K, more Ag atoms occupy interstitial positions to provide excess electrons for the system, resulting in a higher carrier concentration than the Pb 1.01 Te sample. It is noteworthy that the carrier mobilities of Pb 1.01 Te + Ag at high temperatures are also higher than those of Pb 1.01 Te, which can be explained by the suppressed bipolar effect. As a result, the carrier mobility of Pb 1.01 Te + Ag is greater than that of Pb 1.01 Te in the entire temperature range.
To further reveal the role of Ag in PbTe, we utilized first principles to calculate various defects and their formation energy in the system, such as vacancies, interstitials, antisites, and Ag-filled intrinsic vacancies. Figure 4d depicts the calculated formation energy of related defects. Based on the existence of Pb vacancies, the formation energy of Pb vacancies in the Pb-rich system is greater than that in the Te-rich system, implying that Pb vacancies are more difficult to form in the Pbrich condition. For Pb 1.01 Te (Pb-rich system), the formation energy of Ag Pb (Ag-occupied Pb vacancies) is lower than that of V Pb (Pb vacancies), indicating that the introduction of Ag reduces the Pb vacancies, thereby lowering the content of point defects and improving the carrier mobility. The formation energy of Ag i (Ag interstitials) is also very low in both Pb-rich and Te-rich systems, demonstrating that Ag not only fills Pb vacancies but also occupies the interstitials in PbTe. The calculated results of defect formation energy well support the experimental results and verify the role of the Ag element in improving the electrical transport performance of the Pb 1.01 Te system. Thermal Transport Performance of Pb 1.01 Te + xAg. Figure 5 displays the temperature-dependent thermal properties of Pb 1.01 Te + xAg. In Figure 5a, the total thermal conductivity decreases slightly. The electronic thermal conductivity is calculated from equation κ ele = LσT (L is the Lorenz number, as shown in Figure S7a, determined by the single parabolic band (SPB) model). Because of the greater electrical conductivity, the Pb 1.01 Te + xAg system displays much higher electronic thermal conductivity than Pb 1.01 Te, as shown in Figure 5b. Figure 5c presents the lattice thermal conductivity κ lat calculated by κ lat = κ tot − κ ele as a function of temperature. In the high-temperature region, all of the Pb 1.01 Te + xAg samples exhibit lower κ lat than Pb 1.01 Te since the elevated electronic thermal conductivity of Pb 1.01 Te + xAg effectively suppresses the bipolar diffusion. Excess Ag depresses the minimum lattice thermal conductivity from ∼1.2 Wm −1 K −1 for Pb 1.01 Te to ∼0.7 Wm −1 K −1 for Pb 1.01 Te + 0.005Ag. The solid black line in Figure 5c   where A is the constant and E g is the band gap. Ag enlarges the band gap in Figure 5d, thereby reducing the bipolar thermal conductivity. The (κ tot − κ ele ) − 1000 T −1 relationship is plotted in Figure 5e to examine the contribution of bipolar thermal conductivity, revealing that the true lattice thermal conductivity should be a straight line, while the κ tot − κ ele values in the high-temperature region are higher than the predicted values, indicating that bipolar diffusion occurs in this region. According to Figure 5f, bipolar thermal conductivity is the difference between the solid line and the dotted line and decreases as the amount of Ag increases. ZT Values of Pb 1.01 Te + xAg. Comparing room-temperature carrier mobility of the Pb 1.01 Te + xAg system with those of the other n-type PbTe materials, we found that this system exhibits superior carrier mobility of ∼7300 cm 2 V −1 s −1 at low carrier concentrations (∼10 17 cm −3 ), as shown in Figure 6a, which is competitive in high-performance n-type PbTe-based materials. Finally, as a result of ultrahigh carrier mobility and suppressed bipolar thermal conductivity, room-temperature ZT, as shown in Figure 6b, is further enhanced from ∼0.5 for Pb 1.01 Te to ∼0.6 for Pb 1.01 Te + 0.002Ag, and high-temperature ZT is significantly increased from ∼0.5 for Pb 1.01 Te to ∼1.3 for Pb 1.01 Te + 0.004Ag.
Thermoelectric Transport Performance of Pb 1.01 Te 1−x I x + 0.002Ag. Based on Pb 1.01 Te + 0.002Ag with the maximum average ZT, I doping is employed to increase the carrier concentration, thereby improving the electrical performance. Figure S8 shows the phase identification of Pb 1.01 Te 1−x I x + 0.002Ag (x = 0−0.003). No new peak is found in Figure S8a, and the samples still denote the NaCl structure. The lattice parameter decreases slightly in Pb 1.01 Te 1−x I x + 0.002Ag, as shown in Figure S8b, because smaller I − (∼2.06 Å) substitutes for larger Te 2− (∼2.11 Å). Figure 7 depicts the thermoelectric performance of Pb 1.01 Te 1−x I x + 0.002Ag (x = 0−0.003). I doping can effectively improve the electrical conductivity, as shown in    Figure 7a. The room-temperature electrical conductivity can be magnified from ∼633.5 S cm −1 for Pb 1.01 Te + 0.002Ag to ∼3267.8 S cm −1 for Pb 1.01 Te 0.998 I 0.002 + 0.002Ag. The Seebeck coefficients of all samples in Figure 7b are negative, showing ntype semiconductor characteristics. The absolute value of the Seebeck coefficient of Pb 1.01 Te 1−x I x + 0.002Ag decreases with increasing doping amount of the I element since the more I content, the higher the carrier concentration, as shown in Figure S9. The high electrical conductivity and low Seebeck coefficient of the Pb 1.01 Te 1−x I x + 0.002Ag system indicate that the I element possesses extremely high doping efficiency in PbTe. The carrier concentration can be efficiently increased by doping with as little as 0.002I. Figure 7c shows that the power factor increases across the entire temperature range, with the maximum power factor increasing from ∼39.3 μW cm −1 K −2 for Pb 1.01 Te + 0.002Ag to ∼48.5 μW cm −1 K −2 for Pb 1.01 Te 0.998 I 0.002 + 0.002Ag. The average power factor exceeds ∼30.0 μW cm −1 K −2 for Pb 1.01 Te 0.998 I 0.002 + 0.002Ag, which is higher than those of other n-type PbTe systems (PbTe−S−I, 47 PbTe−Sb 2 Te 3 −Sb−Cu 2 Te, 23 Ag n Pb 100 InTe 100+2n , 48 PbTe + Cu, 49 PbTe−GeTe, 50 PbTe−MnTe, 51 PbTe−Ga 52 ), as shown in Figure 7d. In Figure 7e, the total thermal conductivity of Pb 1.01 Te 1−x I x + 0.002Ag increases with increasing I content, primarily owing to an enhancement in electronic thermal conductivity. The lattice thermal conductivity decreases with increasing I content, as shown in Figure 7f, due to the enhanced phonon scattering. The minimum lattice thermal conductivity is reduced to ∼0.5 Wm − 1 K − 1 for Pb 1.01 Te 0.998 I 0.002 + 0.002Ag.
To comprehensively evaluate the thermoelectric performance of the Pb 1.01 Te 1−x I x + 0.002Ag system, the relationship between carrier concentration and the ratio of carrier mobility to lattice thermal conductivity (μ/κ lat ) is plotted, as shown in Figure 8a. Compared with other high-performance n-type PbTe systems (PbTe−S−I, 47 PbTe−Sb 2 Te 3 −Sb−Cu 2 Te, 23 Ag n Pb 100 InTe 100+2n , 48 PbTe + Cu, 49 PbTe−GeTe, 50 PbTe− MnTe, 51 PbTe−Ga 52 ), the Pb 1.01 Te 1−x I x + 0.002Ag system possesses higher μ/κ lat values at lower carrier concentrations, indicating that a trace of Pb atoms (Pb-occupied Pb vacancies) and Ag atoms (Ag-occupied Pb vacancies) can effectively regulate the intrinsic defects in PbTe and reduce the scattering for charge carriers, protecting the charge carrier transport while scattering phonon. Accordingly, owing to a better balance between electrons and phonons, the ZT value increases in the whole temperature range, and the maximum ZT value is enhanced from ∼1.2 for Pb 1.01 Te + 0.002Ag to ∼1.5 for Pb 1.01 Te 0.998 I 0.002 + 0.002Ag, as shown in Figure 8b. Figure 8c,

■ CONCLUSIONS
This work has provided a deeper insight into designing finetuned defects to improve the carrier mobility of n-type PbTe. In particular, by introducing a small amount of Pb, the reduced Pb vacancy improves the carrier mobility to ∼3400 cm 2 V −1 s −1 at 300 K for Pb 1.01 Te. Then, the room-temperature carrier mobility can reach as high as ∼7300 cm 2 V −1 s −1 for Pb 1.01 Te + 0.002Ag due to Ag-induced dynamic doping. Finally, Iodine doping dramatically increases the carrier concentration while maintaining superior carrier mobility compared to other PbTe systems with only traditional dopants. The combination of high carrier mobility and the suppressed bipolar effect enables the significant enhancement of thermoelectric performance with a high ZT ∼1.5 at 773 K and average ZT ave ∼1.0 at 300− 773 K for n-type Pb 1.01 Te 0.998 I 0.002 + 0.002Ag. These findings provide insights into balancing electron and phonon transport via fine tuning of defects, which could be a promising aspect of co-optimizing thermal and electrical performance of materials with instinct defects. ■ ASSOCIATED CONTENT